Area-efficient algorithms for straight-line tree drawings

Computational Geometry: Theory and Applications

Volumn 15, Issue 4, 2000, Pages 175-202

  Shin, Chan Su ^a   Kim, Sung Kwon ^b   Chwa, Kyung Yong ^a  

^a Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

^b Chung Ang University   (South Korea)

Author keywords

Aspect ratio; Drawing area; Graph drawing; Layout; Tree drawing

Indexed keywords

EID: 0347646677     PISSN: 09257721     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0925-7721(99)00053-X     Document Type: Article

References (28)

1. L. Alonso, R. Schott, Random Generation of Trees, Kluwer Academic Publishers, Dordrecht, 1995.
2. S.N. Bhatt, F.T. Leighton, A framework for solving VLSI graph layout problems, J. Comput. Syst. Sci. 28 (1984) 300-343.
3. T. Chan, A near-linear area bound for drawing binary trees, in: Proc. 10th ACM-SIAM Symp. on Discrete Algorithms, 1999.
4. T. Chan, M.T. Goodrich, S.R. Kosaraju, R. Tamassia, Optimizing area and aspect ratio in straight-line orthogonal tree drawings, in: S. North (Ed.), Graph Drawing (Proc. GD '96), Lecture Notes in Computer Science, Vol. 1353, Springer, Berlin, 1997.
5. R.F. Cohen, P. Eades, T. Lin, F. Ruskey, Three-dimensional graph drawing, in: R. Tamassia, I.G. Tollis (Eds.), Proc. Graph Drawing: DIMACS International Workshop, GD'94, Lecture Notes in Computer Science, Vol. 894, Springer, Berlin, 1994, pp. 1-11.
6. T.H. Cormen, C.E. Leiserson, R.L. Rivest, Introduction to Algorithms, MIT Press, Cambridge, MA, 1990.
7. P. Crescenzi, G. Di Battista, A. Piperno, A note on optimal area algorithms for upward drawings of binary trees, Computational Geometry 2 (1992) 187-200.
8. P. Crescenzi, P. Penna, Strictly-upward drawings of ordered search trees, Theoret. Comput. Sci. 203 (1998) 51-67.
9. P. Crescenzi, P. Penna, A. Piperno, Linear area upward drawings of AVL trees, Computational Geometry 9 (1998) 25-42 (Special Issue on Geometric Representations of Graphs, edited by G. Di Battista and R. Tamassia).
10. G. Di Battista, P. Eades, R. Tamassia, I.G. Tollis, Algorithms for drawing graphs: an annotated bibliography, Computational Geometry 4 (1994) 235-282.
11. P. Eades, T. Lin, X. Lin, Minimum size h-v drawings, in: Proc. Advanced Visual Interfaces, World Scientific Series in Computer Science, Vol. 36, 1992, pp. 386-394.
12. A. Garg, M.T. Goodrich, R. Tamassia, Area-efficient upward tree drawings, in: Proc. 9th Ann. ACM Symp. Comput. Geom., 1993, pp. 359-368.
13. H. Gazit, G.L. Miller, S.-H. Teng, Optimal tree contraction in an EREW model, in: S.K. Tewksbury, B.W. Dickinson, S.C. Schwartz (Eds.), Concurrent Computations: Algorithms, Architecture and Technology, Plenum Press, New York, 1988, pp. 139-156.
14. R.L. Graham, D.E. Knuth, O. Patashnik, Concrete Mathematics, Addison-Wesley, Reading, MA, 1989.
15. L.J. Guibas, J. Hershberger, D. Leven, M. Sharir, R.E. Tarjan, A linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons, Algorithmica 2 (1987) 209-233.
16. S.K. Kim, Simple algorithms for orthogonal upward drawings of binary and ternary trees, in: Proc. 7th Canadian Conference on Computational Geometry, 1995, pp. 115-120.
17. S.K. Kim, Logarithmic width, linear area upward drawing of AVL trees, in: Inform. Process. Lett. 63 (1997) 303-307.
18. F.T. Leighton, A. Rosenberg, 3D circuit layouts, SIAM J. Comput. 15 (1986) 793-813.
19. C.E. Leiserson, Area Efficient VLSI Computation, MIT Press, Cambridge, MA, 1983.
20. R.J. Lipton, R.E. Tarjan, Applications of a planar separator theorem, SIAM J. Comput. 9 (1980) 615-627.
21. K. Mehlhorn, Data Structures and Algorithms 1: Sorting and Searching, Springer, Berlin, 1984.
22. M.H. Overmars, The Design of Dynamic Data Structures, Lecture Notes in Computer Science, Vol. 156, Springer, Heidelberg, Germany, 1983.
23. Y. Shiloach, Arrangements of planar graphs on the planar lattice, Ph.D. Thesis, Weizmann Institute of Science, 1976.
24. C.-S. Shin, S.K. Kim, K.-Y. Chwa, Area-efficient algorithms for upward straight-line tree drawings, in: The 2nd International Computing and Combinatorics Conference (COCOON'96), Lecture Notes in Computer Science, Vol. 1090, Springer, Berlin, 1996, pp. 106-116.
25. C.-S. Shin, S.K. Kim, K.-Y. Chwa, Algorithms for drawing binary trees in the plane, Inform. Process. Lett. 66 (3) (1998) 133-139.
26. R. Tamassia, Graph drawing, in: J.E. Goodman, J. O'Rourke (Eds.), Handbook of Discrete and Computational Geometry, CRC Press, Boca Raton, FL, 1997, Chapter 44, pp. 815-832.
27. J.D. Ullman, Computational Aspects of VLSI, Morgan Kaufmann, San Mateo, CA, 1992.
28. L.G. Valiant, Universality considerations of VLSI circuits, IEEE Trans. Comput. 30 (12) (1981) 135-140.